Local refinement in non-overlapping domain decomposition
by
Vesselin A. Dobrev
Central Laboratory of Parallel Processing, Bulgarian Academy of Sciences

Given a partitioning of the domain into non-overlapping subdomains a finite element space is constructed that allows for different levels of refinement in the subdomains, that is in each subdomain the mesh is obtained by several steps of uniform refinement from an initial coarse mesh. The resulting spaces are conformed by suitable interface space (space on the boundaries of the subdomains) properly extended into the subdomains. An error estimate for the approximation properties of the resulting discrete space is presented. Naturally, this discretization is suitable for parallel computations as it is domain decomposition discretization. For the stability of the interface-subdomains splitting a bounded extension operator from the interface into the subdomains is required. Examples of such computationally feasible extension mappings are given and implemented in the numerical experiments. The preconditioning of a discrete system corresponding to the constructed finite element space requires appropriate subdomain and interface preconditioners. Numerical experiments for elasticity problem with large jumps of the Lame coefficients in parallelepiped domain are presented. In order to get better approximation, local refinement as described above is used. The results for this discretization are presented and compared to the results obtained from uniform multilevel discretization.

Date received: February 1, 2000